"... Nonhomomorphicity is a new nonlinearity characterization of a mapping or S-box. An important advantage of nonhomomorphicity over other criteria is that it is easy to estimate by a fast statistical method with a high reliability due to the Law of Large Numbers In this paper we explicitly express the ..."

Nonhomomorphicity is a new nonlinearity characterization of a mapping or S-box. An important advantage of nonhomomorphicity over other criteria is that it is easy to estimate by a fast statistical method with a high reliability due to the Law of Large Numbers In this paper we explicitly express the kth-order nonhomomorphicity of Sboxes by other criteria, identify the tight upper and lower bounds of nonhomomorphicity and nd the mean of nonhomomorphicity over all the S-boxes with the same size. All the results are useful in analysis of S-boxes.